I have three year squaretrade warranty with accidental damage for my iPad 1 and I still bought AppleCare right before my first free year expired. My iPad 1 had weird screen defects that didn't start appearing until 10 months of use (before that the screen was perfect). With squaretrade I would have had to file a claim, send them my iPad, wait for them to receive and analyze it, then wait for them to either fix/ship it back or send me a check for the cost of the iPad. With AppleCare I made an appointment at the closest Apple store, brought them my iPad, showed them the problem, and walked out with a swapped iPad. No waiting, no time where I was without an iPad, simple and easy.
AppleCare can only be extended a year and doesn't cover accidental damage so I'm still keeping the squaretrade warranty, but the convenience of dealing with AppleCare makes it worth a double-dip.